Extrapolation of Stationary Random Fields Via Level Sets

TL;DR

This paper introduces a novel method for extrapolating stationary random fields using excursion sets, optimizing the similarity between the field and its predictor by minimizing the expected volume of their symmetric difference, demonstrated on Gaussian fields.

Contribution

It proposes a new excursion set-based approach for extrapolating stationary random fields, linking the field and predictor through volume minimization of their symmetric difference.

Findings

Effective extrapolation demonstrated on Gaussian random fields

New approach links excursion sets with field prediction accuracy

Minimizes expected volume of symmetric difference for better predictions

Abstract

In this paper, we use the concept of excursion sets for the extrapolation of stationary random fields. Doing so, we define excursion sets for the field and its linear predictor, and then minimize the expected volume of the symmetric difference of these sets under the condition that the univariate distributions of the predictor and of the field itself coincide. We illustrate the new approach on Gaussian random fields.